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Set Covering by Single-Branch Enumeration with Linear-Programming Subproblems

Author

Listed:
  • C. E. Lemke

    (Rensselaer Polytechnic Institute, Troy, New York)

  • H. M. Salkin

    (Case Western Reserve University, Cleveland, Ohio)

  • K. Spielberg

    (IBM Research Center, Yorktown Heights, New York)

Abstract

This paper presents an algorithm for the set-covering problem (that is, min c ′ y : Ey ≧ e , y ≧ 0, y i integer, where E is an m by n matrix of l's and 0's, and e is an m -vector of l's). The special problem structure permits a rather efficient, yet simple, solution procedure that is basically a (0, 1) search of the single-branch type coupled with linear programming and a suboptimization technique. The algorithm has been found to be highly effective for a good number of relatively large problems. Problems from 30 to 905 variables with as many as 200 rows have been solved in less than 16 minutes on an IBM 360 Model 50 computer. The algorithm's effectiveness stems from an efficient suboptimization procedure, which constructs excellent integer solutions from the solutions to linear-programming subproblems.

Suggested Citation

  • C. E. Lemke & H. M. Salkin & K. Spielberg, 1971. "Set Covering by Single-Branch Enumeration with Linear-Programming Subproblems," Operations Research, INFORMS, vol. 19(4), pages 998-1022, August.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:4:p:998-1022
    DOI: 10.1287/opre.19.4.998
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    Cited by:

    1. Rabinowitz, Gad, 1997. "A shrunken cyclic inspection schedule for deteriorating production stages," European Journal of Operational Research, Elsevier, vol. 96(3), pages 493-503, February.
    2. Monique Guignard & Ellis Johnson & Kurt Spielberg, 2005. "Logical Processing for Integer Programming," Annals of Operations Research, Springer, vol. 140(1), pages 263-304, November.

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